Astronomy Practice Exam

What does conservation of angular momentum suggest about rotating objects?

1. Angular momentum decreases when the speed increases.

2. Objects rotate faster as they shrink in radius.

3. The angular momentum of an object cannot change under any circumstances.

4. Objects lose kinetic energy as they rotate.

The correct answer is: Objects rotate faster as they shrink in radius.

The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of that system remains constant. This principle has significant implications for rotating objects. When an object changes its moment of inertia—such as when it shrinks in radius—its rotational velocity must adjust to ensure that the angular momentum remains constant. Angular momentum (L) is defined as the product of the moment of inertia (I) and the angular velocity (ω): L = Iω. If the radius of a rotating object decreases (and thus its moment of inertia decreases), the angular velocity must increase to maintain the value of angular momentum. This is why it is observed that as an object shrinks in radius, it rotates faster. This concept can be visually understood by considering ice skaters. When they pull their arms in while spinning, they reduce their radius, resulting in a faster rotation. Thus, the idea that objects rotate faster as they shrink in radius aligns perfectly with the conservation of angular momentum.